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A233587
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Coefficients of the generalized continued fraction expansion sqrt(7) = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).
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11
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2, 3, 30, 34, 111, 235, 3775, 5052, 7352, 9091, 34991, 35530, 53424, 57290, 66023, 1409179, 1519111, 1725990, 1812396, 4370835, 4507156, 4655396, 44257080, 234755198, 261519946, 264374278, 273487975
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OFFSET
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1,1
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COMMENTS
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For more details on Blazys' expansions, see A233582.
Sqrt(7) is the first square root of a natural number with an a-periodic Blazys' expansion (see A233592 and A233593).
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LINKS
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FORMULA
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sqrt(7) = 2+2/(3+3/(30+30/(34+34/(111+...)))).
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MATHEMATICA
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BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[Sqrt@7, 32] (* Robert G. Wilson v, May 22 2014 *)
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PROG
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(PARI) bx(x, nmax)={local(c, v, k); // Blazys expansion function
v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }
bx(sqrt(7), 1000) // Execution; use very high real precision
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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